We carried out a systematic search of precursors on the sample of short GRBs observed by Swift. We found that approx. 8-10% of short GRBs display such early episode of emission. One burst (GRB 090510) shows two precursor events, the former approx.13 s and the latter approx. 0.5 s before the GRB. We did not find any substantial difference between the precursor and the main GRB emission, and between short GRBs with and without precursors. We discuss possible mechanisms to reproduce the observed precursor emission within the scenario of compact object mergers. The implications of our results on quantum gravity constraints are also discussed.